Theoretical probability is the probability of an event occurring based on mathematical counting techniques. Under ideal conditions, theoretical probability describes what we expect to happen in the long run. Experimental probability is the estimated probability based on observations made during an experiment. It is important that we understand that the experimental probability of an event approaches that of the theoretical probability of the event as the number of trials (observations) in the experiment increases.

Many times we can use the techniques of experimental probability to model a situation that may be difficult or even impossible to observe in real life by conducting a simulation. We can model these situations using easy tools (devices), such as number cubes, coins, or spinners or technology, such as calculators. We can also conduct a survey, in which people are asked questions whose responses are used to determine the probability of an event occurring. This is another example of the use of experimental probability.

Students can be given the results of a survey or simulation and be asked to make a prediction based on the given data.

Natasha surveys her class to determine the favorite sport of her classmates. The results are shown below.

Based on the given data, what is the probability that the next student would like gymnastics?

Sample correct response: Using the survey data, 9 students out of 30 preferred gymnastics. Since this data is to be used to make the prediction, the probability that the next student would like gymnastics is 9 out of 30, which can be expressed as 9 out of 30, 3 out of 10, 30%, 0.30, , or .

The Central Warriors and the Middle River Mavericks are playing a five game basketball tournament. The team that wins two of the three games is the winner. The two teams are evenly matched. Use a coin toss to simulate playing one game. Let heads represent a win for the Warriors and tails represent a win for the Mavericks. You will toss the coin five times to represent the playing of the five-game tournament. For each toss you will record the winner. Repeat the simulation of the tournament 20 times. Record your results in the chart.

What is the probability that the Warriors will win the tournament based on your simulation?

Sample correct answer: The Warriors may have won 11 of the 20 tournaments. Based on the experimental data, the probability that the Warriors will win the actual tournament is or .55 or 55%.
 

How does this compare to the theoretical probability that the Warriors will win the tournament?

Sample correct answer: The Warriors and the Mavericks are evenly matched. Theoretically, the Warriors have a 1 out of 2 chance of winning the actual tournament. P(W) = or .5 or 50%.